The design of novel microsystems that include active (smart/intelligent) materials with responsiveness to various stimuli - e.g., electrical, magnetic, thermal, light, optical, or chemical concentrations - relies on an adequate representation of the coupled multi-field interactions. Based on the modeling and simulation of systems at different abstraction levels, new components with stimulus-responsivity can be invented and adapted to complement MEMS approaches. The current work aims at giving an overview over various modeling approaches, comprising continuum-based multifield models, equivalent circuit descriptions and machine learning based (data-driven) approaches. At the example of a microfluidic array system, a hierarchical chain of models over the abstraction levels is discussed. Furthermore, guidelines for selecting the most efficient model approach are presented. We thus bring together the viewpoints of continuum mechanics based modeling and network based approaches and establish a common vocabulary that spans from material science to system engineering.